Numerous positive displacement machines with planetary motion that match this description are known. Essentially, the machines that are described in the article entitled "Projektieren der Zykloidenverzahnungen hydraulischer Verdrangermaschinen" [Design of Cycloidal Gears in Hydraulic Machines], in Mechanism and Machine Theory, Vol. 25, No. 6, 1990, may be mentioned.
It will be observed that in these planetary-motion machines, in order to specify a value of s.sub.P differing from each other by one, the axis of the cylindrical surface defining the outer shape of the piston must be coincident with the axis of its rotoidal connection with the third device. Moreover, in the machines in which the value of s.sub.C differs from each other by one, the axis of the cylindrical surface defining the inside shape of the enclosure must be coincident with the axis of its rotoidal connection with the third device. When s.sub.P =1, the axis of the cylindrical surface defining the outer shape of the piston may be selected arbitrarily, on the condition that it is parallel to the axes of the third device. When s.sub.C =1, the axis of the cylindrical surface defining the inside shape of the enclosure may be selected arbitrarily, providing it is parallel to one of the axes of the third device.
Positive displacement planetary-motion machines described in the article above are distinguished from machines according to the invention by the geometry of the enclosure and of the piston. In fact, in the existing machines either the piston or the enclosure has a directrix which is a curtate hypotrochoid or epitrochoid, or a curve uniformly distant from a non-prolate (that is, ordinary or curtate) hypotrochoid or epitrochoid. All these curves have only one or two formal parameters, which cannot be selected except within narrow limits. Using these curves, it is not possible to meet all the desirable technological constraints in modern machines.